Technical Field
The present invention relates to automatic model discovery and, more particularly, combining data-driven methods with primitives of first-principles based modeling to generate a mathematical model.
Description of the Related Art
Mathematical modeling provides a consistent link between the input and output of a system or phenomenon under investigation. These models are used for various objectives such as description, prediction, and design, through a broad range of science and engineering disciplines, including physics, chemistry, biology, economics, etc. Historically, researchers and practitioners find consistent and generalized cause and effect links through experiment and formulate mathematical expressions that embody such relations. However, modeling complex phenomena, in particular while relying on a relatively small number of observations, is difficult to accomplish.
Traditionally the formulation of mathematical models is attempted through first principles formulations, using modeling primitives such as differential operators and integral equations. Such an approach benefits from great generality in the governing relations, but identification of an appropriate formulation is non-trivial. Such an approach usually relies on human intuition and the frequently tedious comparison of predictions with experimental observations.
At the other extreme, modeling can be performed using data driven approaches that use generic statistical models, assuming that a sufficient amount of input data is provided. Statistical models may be limited in their generalizability and, depending on the capacity and complexity of the predictive relation in the prescribed functional form, may require an intractably large set of examples to use as training data.